Competitive numerical analysis for stochastic HIV/AIDS epidemic model in a two‐sex population |
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| Authors: | Ali Raza Muhammad Rafiq Dumitru Baleanu Muhammad Shoaib Arif Muhammad Naveed Kaleem Ashraf |
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| Affiliation: | 1. Stochastic Analysis and Optimization Research Group, Department of Mathematics, Air University, PAF Complex E-9, Islamabad Pakistan ; 2. Faculty of Engineering, University of Central Punjab, Lahore Pakistan ; 3. Department of Mathematics, Cankaya University, 06530, Balgat, Ankara Turkey ; 4. Institute of Space Sciences, Magurele-Bucharest, Romania ; 5. Department of Mathematics, University of Management and Technology, Lahore Pakistan |
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| Abstract: | This study is an attempt to explain a reliable numerical analysis of a stochastic HIV/AIDS model in a two‐sex population considering counselling and antiretroviral therapy (ART). The authors are comparing the solutions of the stochastic and deterministic HIV/AIDS epidemic model. Here, an endeavour has been made to explain the stochastic HIV/AIDS epidemic model is comparatively more pragmatic in contrast with the deterministic HIV/AIDS epidemic model. The effect of threshold number H * holds on the stochastic HIV/AIDS epidemic model. If H * < 1 then condition helps us to control disease in a two‐sex human population while H * > 1 explains the persistence of disease in the two‐sex human population. Lamentably, numerical methods such as Euler–Maruyama, stochastic Euler, and stochastic Runge–Kutta do not work for large time step sizes. The recommended structure preserving framework of the stochastic non‐standard finite difference (SNSFD) scheme conserve all vital characteristics such as positivity, boundedness, and dynamical consistency defined by Mickens. The effectiveness of counselling and ART may control HIV/AIDS in a two‐sex population.Inspec keywords: diseases, stochastic processes, epidemics, patient treatment, finite difference methodsOther keywords: two‐sex human population, antiretroviral therapy, competitive numerical analysis, stochastic HIV‐AIDS epidemic model, structure preserving framework, stochastic nonstandard finite difference scheme, SNSFD scheme, deterministic HIV‐AIDS epidemic model |
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